Related papers: A General Framework for Equivariant Neural Network…
Simulation-based inference with conditional neural density estimators is a powerful approach to solving inverse problems in science. However, these methods typically treat the underlying forward model as a black box, with no way to exploit…
Efficient transfer learning algorithms are key to the success of foundation models on diverse downstream tasks even with limited data. Recent works of Basu et al. (2023) and Kaba et al. (2022) propose group averaging (equitune) and…
We introduce a class of fully-connected neural networks whose activation functions, rather than being pointwise, rescale feature vectors by a function depending only on their norm. We call such networks radial neural networks, extending…
We present a finite algorithm for computing the set of irreducible unitary representations of a real reductive group G. The Langlands classification, as formulated by Knapp and Zuckerman, exhibits any representation with an invariant…
In this paper we show how Group Equivariant Convolutional Neural Networks use subsampling to learn to break equivariance to their symmetries. We focus on 2D rotations and reflections and investigate the impact of broken equivariance on…
Content and image generation consist in creating or generating data from noisy information by extracting specific features such as texture, edges, and other thin image structures. We are interested here in generative models, and two main…
Incorporating Euclidean symmetries (e.g. rotation equivariance) as inductive biases into graph neural networks has improved their generalization ability and data efficiency in unbounded physical dynamics modeling. However, in various…
We introduce ChebLieNet, a group-equivariant method on (anisotropic) manifolds. Surfing on the success of graph- and group-based neural networks, we take advantage of the recent developments in the geometric deep learning field to derive a…
Several problems in number theory when reformulated in terms of homogenous dynamics involve study of limiting distributions of translates of algebraically defined measures on orbits of reductive groups. The general non-divergence and…
This paper presents RadioGUNet, a UNet-based deep learning framework for pathloss estimation in wireless communication. Unlike other frameworks, it leverages group equivariant convolutional networks, which are known to increase the…
We reconstruct a quantum group associated with any Lie algebra together with its representation theory from twisted homologies of generalized configuration spaces of disks. Along the way it brings new combinatorics to the theory, but our…
Symmetry lies at the heart of todays theoretical study of particle physics. Our manuscript is a tutorial introducing foundational mathematics for understanding physical symmetries. We start from basic group theory and representation theory.…
Physical theories grounded in mathematical symmetries are an essential component of our understanding of a wide range of properties of the universe. Similarly, in the domain of machine learning, an awareness of symmetries such as rotation…
Many machine learning tasks involve learning functions that are known to be invariant or equivariant to certain symmetries of the input data. However, it is often challenging to design neural network architectures that respect these…
We provide new stable linearizability constructions for regular actions of finite groups on homogeneous spaces and low-dimensional quadrics.
This article shows that one can consistently incorporate nonunitary representations of at least one group into the ``ordinary'' nonrelativistic quantum mechanics. This group turns out to be Lorentz group thus giving us an alternative…
In Gen. Rel. Grav. (36, 111-126 (2004); in press, gr-qc/0410010) we have proposed a model unifying general relativity and quantum mechanics based on a noncommutative geometry. This geometry was developed in terms of a noncommutative algebra…
We develop an elementary method to compute spaces of equivariant maps from a homogeneous space $G/H$ of a Lie group $G$ to a module of this group. The Lie group is not required to be compact. More generally, we study spaces of invariant…
In this survey, we report on the state of the art of some of the fundamental problems in the Lie theory of Lie groups modeled on locally convex spaces, such as integrability of Lie algebras, integrability of Lie subalgebras to Lie…
We obtain the $\rm{p4m}$-symmetric Group Convolutional Neural Network (GCNN) representations of the lowest energy eigenstate of the quantum dimer model on $L{\times} L$ square-lattice in each of the ${(L^2+18L+72)}/{8}$ irreducible…